相关论文: Metric for attractor overlap

The properties of the mean first passage time in a system characterized by multiple periodic attractors are studied. Using a transformation from a high dimensional space to 1D, the problem is reduced to a stochastic process along the path…

We investigate aspects of low-magnetic-Reynolds-number flow between two parallel, perfectly insulating walls, in the presence of an imposed magnetic field parallel to the bounding walls. We find a functional basis to describe the flow, well…

We propose a data-driven methodology to learn a low-dimensional manifold of controlled flows. The starting point is resolving snapshot flow data for a representative ensemble of actuations. Key enablers for the actuation manifold are…

Since the year 2000, adaptive optics (AO) has seen the emergence of a variety of new concepts addressing particular science needs; multiconjugate adaptive optics (MCAO) is one of them. By correcting the atmospheric turbulence in 3D using…

The retrieval abilities of spatially uniform attractor networks can be measured by the average overlap between patterns and neural states. We found that metric networks, with local connections, however, can carry information structured in…

This paper presents a simple periodic parameter-switching method which can find any stable limit cycle that can be numerically approximated in a generalized Duffing system. In this method, the initial value problem of the system is…

We present a fully automated method that identifies attractors and their basins of attraction without approximations of the dynamics. The method works by defining a finite state machine on top of the system flow. The input to the method is…

Integrated task and motion planning problems describe a multi-modal state space, which is often abstracted as a set of smooth manifolds that are connected via sets of transitions states. One approach to solving such problems is to sample…

Multi-view multi-instance feature association constitutes a crucial step in 3D reconstruction, facilitating the consistent grouping of object instances across various camera perspectives. The presence of multiple identical objects within a…

In this paper, a two parameters family $F_{\beta_1,\beta_2}$ of maps of the plane living two different subspaces invariant is studied. We observe that, our model exhibits two chaotic attractors $A_i$, $i=0,1$, lying in these invariant…

Uniform manifold approximation and projection (UMAP) is among the most popular neighbor embedding methods. The method samples pairs of point indices according to similarities in the high-dimensional space, and applies attractive and…

We already know a great deal about dynamical systems with uniqueness in forward time. Indeed, flows, semiflows, and maps (both invertible and not) have been studied at length. A view that has proven particularly fruitful is topological:…

We examine a model system where attractors may consist of a heteroclinic cycle between chaotic sets; this `cycling chaos' manifests itself as trajectories that spend increasingly long periods lingering near chaotic invariant sets…

In diverse physical systems stable oscillatory solutions devolve into more complicated dynamical behaviour through border-collision bifurcations. Mathematically these occur when a stable fixed point of a piecewise-smooth map collides with a…

One important frontier for astronomical adaptive optics (AO) involves methods such as Multi-Object AO and Multi-Conjugate AO that have the potential to give a significantly larger field of view than conventional AO techniques. A second key…

The masking-one-out (MOO) procedure, masking an observed entry and comparing it versus its imputed values, is a very common procedure for comparing imputation models. We study the optimum of this procedure and generalize it to a missing…

This paper investigates the asymptotic behavior of the Multi-set Allocation Occupancy (MAO) distribution, which models the count vector $X=(X_{=0},\ldots,X_{=T})$ from $T$ independent rounds of sampling without replacement of size $m$ from…

The paper introduces the class of O-metric spaces, a novel generalization of metric-type spaces, classifying almost all possible metric types into upward and downward O-metrics. We list some topologies arising from O-metrics and discuss…

As the parameters of a map are varied an attractor may vary continuously in the Hausdorff metric. The purpose of this paper is to explore the continuation of chaotic attractors. We argue that this is not a helpful concept for smooth…

We study two-dimensional, two-piece, piecewise-linear maps having two saddle fixed points. Such maps reduce to a four-parameter family and are well known to have a chaotic attractor throughout open regions of parameter space. The purpose of…